Question

An ideal fluid flows through a pipe of circular cross section with diameter $5cm$ and $10cm$ as shown. The ratio of velocities of fluid at $A$ and $B$ is

• A. $4:1$
• B. $1:4$
• C. $2:1$
• D. $1:2$

Answer 1

Answer: (A)

$4:1$

Given : $D_A=5$ cm $D_B=10$ cm

From continuity equation, ratio of velocities:

$\frac{v_A}{v_B}=\frac{A_B}{A_A}=\frac{D_B^2}{D_A^2}$ where $A=\pi D^2$

$⟹$ $v_A:v_B=D_B^2:D_A^2=(10{)}^2:5^2=4:1$